Shape On Animation Path Is Wobbly And Shape Not Facing The Right Direction
If the cube is not animated, the wobbling should be only due to realtime viewport delays, but a true render should be fine.
When you parent or constraint a follow path function, Blender creates a modifier inside the graph editor, generating a straight infinite line. You can delete the modifier and add manual keyframes on the path animation properies tab, knowing that the number of frames (100 in my example) is the value needed to complete the curve, and the evaluation time is the value of the keyframe (so that 50 will mean half path, 33 one third, and so on).